The Mirzakhani function on the moduli space of a surface

Speaker:

Francis Bonahon, University of Southern California

Date and Time:

Wednesday, November 7, 2018 - 11:00am to 12:00pm

Location:

Fields Institute, Room 230

Abstract:

In her famous doctoral work, Maryam Mirzakhani studied the asymptotics of the lengths of multicurves in a hyperbolic surface $X$. These asymptotics are controlled by two constants. The first one depends only on the topological type of the surface and of the multicurves considered. The second constant $\mu(X)$ depends on the hyperbolic metric of $X$, and is defined as the Thurston volume of the set of measured geodesic laminations of length at most $1$. I will discuss properties of $\mu(X)$ as a function on the moduli space of hyperbolic metrics on a given surface. The emphasis will be on the case of the one-punctured torus, as well as on experimental data and pretty pictures. This is joint work with Sabrina Enriquez, then an undergraduate at USC.

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